Some conventional feedback control strategies for flying air vehicles may use Euler pitch as a mechanism to control airspeed and Euler roll to control bank angle. For hovering vehicles, such as, for example, a helicopter, body pitch and body roll are used for controlling forward and side speed. In some systems, Euler pitch error may be mapped to a control surface that generates a body pitch moment. If, however, the vehicle rolls ninety degrees, using a surface that generates pitch moment will render incorrect results if Euler pitch is the feedback variable. If the vehicle pitches up ninety degrees, Euler angles reach a singularity where Euler roll and Euler heading are not uniquely defined.
An example of a helicopter flight control system is described in U.S. Pat. No. 5,169,090, which attempts to overcome the above-mentioned drawbacks by synchronizing a sensed attitude signal and a desired attitude signal as the pitch attitude of the helicopter approaches ninety degrees to compensate for the Euler singularities. An example of a model-following aircraft control system is described in U.S. Pat. No. 5,617,316, which attempts to overcome the above-mentioned drawbacks by integrating a commanded roll rate in Euler coordinates to provide a bank angle command, which has actual bank angle subtracted therefrom to provide a command error that is converted back to aircraft body coordinates for use, so long as the pitch attitude of the aircraft does not approach zenith or nadir. While the absolute value of the pitch attitude exceeds 85 degrees, the last error generated before exceeding 85 degrees is converted to body coordinates for use by the aircraft, and the initial integrated value of attitude command for use when the pitch angle reverts below 85 degrees is formed as the sum of the last error and the actual attitude angle of the aircraft.
In each of these patents, however, the vehicle being controlled cannot fly nominally at a ninety degree Euler angle for a sustained amount of time, and once another axis such as Euler roll is rotated by ninety degrees, the control actions become incorrect. For example, once a vehicle such as an airplane has banked to ninety degrees, Euler pitch should be controlled by the rudder, where conventional airplane controllers would use the elevator.
In U.S. Pat. No. 5,875,993, a quaternion vector is used to control a thrust vectoring system by converting velocity errors forward and sideways to Euler commands, with Euler roll being a free changing variable. Side velocity error drives Euler heading command and forward velocity error drives Euler pitch command. The output quaternion command is then controlled against a quaternion measured by inertial sensors by applying feedback gain directly to three of the quaternion elements. A method of commanding either Euler angles or forward and North and East velocities and controlling a body attitude of a vehicle at any attitude is disclosed. Once the operating attitude limits are removed, however, Euler angles are no longer adequate control variables. Some have tried to circumvent this problem by using body sensed rates and integrating the body sensed rates over time to achieve body axes attitudes. Although this may render acceptable results under some circumstances, when the absolute attitude is unknown and limits on the attitudes cannot be enforced, this may not be acceptable. Since limiting the operational attitudes of air vehicles is a viable and acceptable option, limited angle controllers fly on many airplanes. For some air vehicles, however, it may be desirable to fly in many different areas of the flight envelope. For example, for a vertical takeoff and landing vehicle that also transitions to forward flight and flies like an airplane, it may be desirable to fly in many different areas of the flight envelope. In such case, limiting the attitudes of the vehicle in flight is not possible.
There may exist a desire to overcome one or more of the above-mentioned drawbacks. The exemplary disclosed systems and methods may seek to satisfy one or more of the above-mentioned drawbacks. Although the presently disclosed systems and methods may obviate one or more of the above-mentioned drawbacks, it should be understood that some aspects of the disclosed systems and methods might not necessarily obviate them.